Mordell Conjecture

References

• Bombieri, Enrico (1990). "The Mordell conjecture revisited". Ann. Scuola Norm. Sup. Pisa Cl. Sci. 17 (4): 615–640. MR 1093712.
• Coleman, Robert F. (1990). "Manin's proof of the Mordell conjecture over function fields". L'Enseignement Mathématique. 2e Série. 36 (3): 393–427. ISSN 0013-8584. MR 1096426.
• Cornell, Gary; Silverman, Joseph H., eds. (1986). Arithmetic geometry. Papers from the conference held at the University of Connecticut, Storrs, Connecticut, July 30 – August 10, 1984. New York: Springer-Verlag. doi:10.1007/978-1-4613-8655-1. ISBN . MR 0861969. → Contains an English translation of Faltings (1983)
• Faltings, Gerd (1983). "Endlichkeitssätze für abelsche Varietäten über Zahlkörpern" [Finiteness theorems for abelian varieties over number fields]. Inventiones Mathematicae (in German). 73 (3): 349–366. Bibcode:1983InMat..73..349F. doi:10.1007/BF01388432. MR 0718935.
• Faltings, Gerd (1984). "Erratum: Endlichkeitssätze für abelsche Varietäten über Zahlkörpern". Inventiones Mathematicae (in German). 75 (2): 381. doi:10.1007/BF01388572. MR 0732554.
• Faltings, Gerd (1991). "Diophantine approximation on abelian varieties". Ann. of Math.133 (3): 549–576. doi:10.2307/2944319. JSTOR 2944319. MR 1109353.
• Faltings, Gerd (1994). "The general case of S. Lang's conjecture". In Cristante, Valentino; Messing, William (eds.). Barsotti Symposium in Algebraic Geometry. Papers from the symposium held in Abano Terme, June 24–27, 1991. Perspectives in Mathematics. San Diego, CA: Academic Press, Inc. ISBN . MR 1307396.
• Grauert, Hans (1965). "Mordells Vermutung über rationale Punkte auf algebraischen Kurven und Funktionenkörper". Publications Mathématiques de l'IHÉS. 25 (25): 131–149. doi:10.1007/BF02684399. ISSN 1618-1913. MR 0222087.
• Hindry, Marc; Silverman, Joseph H. (2000). Diophantine geometry. Graduate Texts in Mathematics. Vol. 201. New York: Springer-Verlag. doi:10.1007/978-1-4612-1210-2. ISBN . MR 1745599. → Gives Vojta's proof of Faltings' Theorem.
• Lang, Serge (1997). Survey of Diophantine geometry. Springer-Verlag. pp. 101–122. ISBN .
• Lawrence, Brian; Venkatesh, Akshay (2020). "Diophantine problems and p-adic period mappings". Invent. Math. 221 (3): 893–999. arXiv:1807.02721. Bibcode:2020InMat.221..893L. doi:10.1007/s00222-020-00966-7.
• Manin, Ju. I. (1963). "Rational points on algebraic curves over function fields". Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya (in Russian). 27: 1395–1440. ISSN 0373-2436. MR 0157971. (Translation: Manin, Yu. (1966). "Rational points on algebraic curves over function fields". American Mathematical Society Translations. Series 2. 59: 189–234. doi:10.1090/trans2/050/11. ISBN . ISSN 0065-9290.{{}}: CS1 maint: periodical has ISBN () )
• McQuillan, Michael (1995). "Division points on semi-abelian varieties". Invent. Math. 120 (1): 143–159. Bibcode:1995InMat.120..143M. doi:10.1007/BF01241125.
• Mordell, Louis J. (1922). "On the rational solutions of the indeterminate equation of the third and fourth degrees". Proc. Cambridge Philos. Soc. 21: 179–192.
• Parshin, A. N. (1970). "Quelques conjectures de finitude en géométrie diophantienne"(PDF). Actes du Congrès International des Mathématiciens. Vol. Tome 1. Nice: Gauthier-Villars (published 1971). pp. 467–471. MR 0427323. Archived from the original(PDF) on 2016-09-24.
• Parshin, A. N. (2001) [1994]. "Mordell conjecture". Encyclopedia of Mathematics. EMS Press.
• Parshin, A. N. (1968). "Algebraic curves over function fields I". Izv. Akad. Nauk SSSR Ser. Mat.32 (5): 1191–1219. Bibcode:1968IzMat...2.1145P. doi:10.1070/IM1968v002n05ABEH000723.
• Shafarevich, I. R. (1963). "Algebraic number fields". Proceedings of the International Congress of Mathematicians: 163–176.
• Vojta, Paul (1991). "Siegel's theorem in the compact case". Ann. of Math.133 (3): 509–548. doi:10.2307/2944318. JSTOR 2944318. MR 1109352.